Which expression is equivalent to (9^4)^3? Choices: (A)1/9^12 (B)1/9^7 (C)9^12 (D)9^7

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. When a power is raised to another power, we multiply the exponents. (a^m)^n = a^(m*n)Apply Rule to Given Expression: Apply the exponent rule to the given expression (9^4)^3. Multiply the exponents 4 and 3. (9^4)^3 = 9^(4*3) = 9^12Compare with Choices: Compare the result with the given choices. The expression 9^12 matches with choice (C) and does not match with any other choices.

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Which expression is equivalent to $(9^4)^3$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{9^{12}}$ $\newline$ (B) $\frac{1}{9^7}$ $\newline$ (C) $9^{12}$ $\newline$ (D) $9^7$

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

(9^4)^3

\newline

Choices:

\newline

(A)

\frac{1}{9^{12}}

\newline

(B)

\frac{1}{9^7}

\newline

(C)

9^{12}

\newline

(D)

9^7

Understand Exponent Rule: Understand the exponent rule for powers raised to powers. $\newline$ When a power is raised to another power, we multiply the exponents. $\newline$ $(a^m)^n = a^{(m*n)}$
Apply Rule to Given Expression: Apply the exponent rule to the given expression $(9^4)^3$ . $\newline$ Multiply the exponents $4$ and $3$ . $\newline$ $(9^4)^3 = 9^{4*3} = 9^{12}$
Compare with Choices: Compare the result with the given choices. $\newline$ The expression $9^{12}$ matches with choice (C) and does not match with any other choices.